Further restrictions on the structure of finite DCI-groups

ǂan ǂaddendum

Edward Dobson (Author), Joy Morris (Author), Pablo Spiga (Author)

Abstract

A finite group ▫$R$▫ is a DCI-group if, whenever ▫$S$▫ and ▫$T$▫ are subsets of ▫$R$▫ with the Cayley digraphs ▫${\mathrm {Cay}}(R, S)$▫ and▫ ${\mathrm{Cay}}(R, T)$▫ isomorphic, there exists an automorphism ▫$\varphi$▫ of ▫$R$▫ with ▫$S^\varphi = T$▫. The classification of DCI-groups is an open problem in the theory of Cayley digraphs and is closely related to the isomorphism problem for digraphs. This paper is a contribution toward this classification, as we show that every dihedral group of order ▫$6p$▫, with ▫$p\geq 5$▫ prime, is a DCI-group. This corrects and completes the proof of C. H. Li et al. [J. Algebr. Comb. 26, No. 2, 161--181 (2007), Theorem 1.1] as observed by the reviewer (Conder in Mathematical Reviews MR2335710).

Keywords

Cayley graph;isomorphism problem;CI-group;dihedral group;

Data

Language:	English
Year of publishing:	2015
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	519.17:412.54
COBISS:	1538038980
ISSN:	0925-9899
Views:	2448
Downloads:	64
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Type (COBISS):	Not categorized
Pages:	str. 959-969
Volume:	ǂVol. ǂ42
Issue:	ǂiss. ǂ4
Chronology:	Dec. 2015
DOI:	10.1007/s10801-015-0612-3
ID:	9159931